how far from an 84 foot burning building should the base of the fire truck ladder be placed to reach the top of the building at an angle of 60 degrees with the ground. the ladder is mounted to the truck 8 ft off the ground
To calculate the distance from the base of the fire truck ladder to the burning building, we can use trigonometry.
First, let's draw a diagram to visualize the situation. The top of the burning building forms a right angle with the ladder, and the ladder forms an angle of 60 degrees with the ground.
Now, let's break down the given information:
- The height of the building is 84 feet.
- The ladder is mounted on the truck at a height of 8 feet off the ground.
To find the distance from the base of the ladder to the building, we need to determine the length of the ladder itself. We can then use the ladder length, along with the 60-degree angle, to find the distance.
Using trigonometric ratios, we can identify that the sine function relates the opposite side (height of the building) to the hypotenuse (length of the ladder). So, we can use the sine function to find the ladder length:
sin(60 degrees) = height of the building / ladder length
Rearranging the equation, we get:
ladder length = height of the building / sin(60 degrees)
Calculating the sine of 60 degrees:
sin(60 degrees) = 0.866
Now, we can substitute the height of the building and the sine value into the equation:
ladder length = 84 feet / 0.866
ladder length ≈ 96.79 feet
Since the ladder is mounted to the truck 8 feet off the ground, the distance from the base of the ladder to the building would be:
Distance = ladder length - height of the truck
Distance = 96.79 feet - 8 feet
Distance ≈ 88.79 feet
Therefore, the base of the fire truck ladder should be placed approximately 88.79 feet away from the burning building to reach the top of the building at a 60-degree angle.